It is not unusual to have outliers and multicollinearity simultaneously in censored semiparametric linear models. In this paper for dealing with multicollinearity and outliers we introduce a family of robust censored Liu and non-Liu type of estimates for the regression parameter when some non-stochastic linear restrictions are imposed. The proposed robust estimators is based on least trimmed squares (LTS) method. The efficiency of LTS estimator statistically is more than the well-known least median squares (LMS) estimator. Unfortunately, the computational complexity of LTS is less well understood than that of LMS in which the objective is to minimize the median squared residual. Here, we provide the robust estimators for linear and non-linear parts of the censored model based on robust shrinkage Liu estimators. The performance of proposed estimators compared to ordinary estimators numerically is evaluated by Monte Carlo simulation studies. We further illustrate our procedures by an application.
